theorem :: FDIFF_9:13

for Z being open Subset of REAL st Z c= dom (cosec * exp_R) holds
( cosec * exp_R is_differentiable_on Z & ( for x being Real st x in Z holds
((cosec * exp_R) `| Z) . x = - (((exp_R . x) * (cos . (exp_R . x))) / ((sin . (exp_R . x)) ^2)) ) )